Black shadows on Faces, not a normals thing
This occurs because you have smooth shading applied to your model. To resolve this, ensure affected topologies are selected, go to the Tool Panel T goto 'Shading' section select 'Flat'.

You can also apply an 'Edge Split' modifier, found under the Modifier tab in Properties Panel. Split edges need to be marked, once selected, with Ctrl + E. Dragging the mouse up/down to define amount.

You may also add more Geometry to the mesh. Either manually with 'Edge Loops' Ctrl+R or by adding a 'Subdivision Surface' modifier, also found in the Modifier tab in Properties Panel.